Making a category not visible for public, read-only for registered users, and editable by certain groups

Unregistered users (those who are not logged-in) shouldn't see the given category

Some users should have full access (read, edit, and delete) to the given category

Other users should be able to have read-only access to the given category

First of all make sure that articles in given category are visible to all logged-in users (set "Public" for Access Restrictions) and invisible for people who haven't logged-in (remove checkbox for Published option).

Make this category restricted to certain groups. Users that belong to these groups will be able to edit this category and articles in it.

When you click "Save & Close" you get a confirmation window. Since we just changing permissions for this category, we remove all checkboxes except "current category".

That's all. Next time you login as a user of a group that doesn't have permission to this category (for example "Group C", or "Group D"), you see that you have read-only access to it and its contents.

If you login as a user of "Group A" or "Group B" you have full access to this category and its articles.

Since articles in this category are not published, non-logged in users do not see them. They do not see this category as well because it is restricted.